The British No 1, who will next face Thomas Muster or Andrei Medvedev, thumped 21 aces to spoil the Swede's 24th birthday with a 2-6 7-6 6-4 victory. Along the way, he beat the service record of 143mph, he set on his way to the US Open final in New York last year to close out the first game of the second set.
The Canadian-born Briton started sluggishly and won only one point in his first two service games before holding to love six times in a row to take a 4-3 lead in the second set. The sixth seed then broke Enqvist in the eighth game of the second set to take a 5-3 lead but a volley error cost him a set point in the next game, which Enqvist went on to win with two passing winners.
In the tie-break, Rusedski netted a backhand to give Enqvist his only point but the unseeded Swede replied by double-faulting to give his opponent set point, and then netted a forehand service return to level the scores.
Rusedski captured the only break of the third set in the fifth game, but had to save a break point in the next to keep his advantage. He served out the match with a love game, Enqvist sending a forehand sailing long on match point.
Muster set up his quarter-final against Medvedev with a stunning 7-5, 6-3 victory over Pete Sampras on Thursday, putting the American's world No 1 status is in doubt. The victory for Muster, a former world No 1 himself, now ranked 20th, means the Australian Open champion, Petr Korda, can take over at the top by winning the title here. Korda, the second seed, beat the German teenager Tommy Haas 7-6, 6-2 to reach the quarter-finals.
Sampras was not the only big name to fall in the third round as Andre Agassi continued his tremendous comeback with a 6-3 3-6 6-2 victory over the third-seeded Australian Pat Rafter, the US Open champion. Agassi will next play the lowest-ranked player left in the draw, the 126th-ranked wild card, Jan-Michael Gambill.
But Sampras' defeat, by a player who had won only one of his three matches all year, eclipsed that upset. "I was awful," Sampras admitted. "I really struggled throughout."
Sampras, the Champions' Cup winner in 1994 and 1995 but a beaten quarter- finalist in 1996 and in the second round last year, said he still had not mastered the desert conditions. "The ball seems to fly on me," he said. "I can't play the way I want to play, can't swing the way I want to swing, and have control."
Muster, who disputed the world No 1 place with Sampras in 1996, and grabbed the top spot for six weeks that year, said he could tell Sampras was struggling. He said: "You always play like your opponent allows you to play. But he wasn't serving as accurate as he used to. He made a lot of unforced errors."
A strained left hamstring ruined Steffi Graf's latest comeback from injury when she retired in the third set of her Evert Cup semi-final with the defending champion, Lindsay Davenport. Graf, who has had a long list of ailments during her career, was trailing 6-4, 4-6, 4-2. Graf was playing in only her second tournament after taking nine months off after knee surgery.
"It's like, what else?" said Graf, whose injuries have included a bad back, bone spurs in her feet and the broken cartilage and torn tendon in her left knee that forced the surgery last June.
A hamstring strain was a new experience. "This one I haven't had before," said Graf, who felt a pain after a sudden movement in the fifth game of the third set. She winced and clutched her thigh, but finished the game. After having her thigh strapped during the change-over, she tried to play, earning a break point against Davenport in the sixth game even though she was hobbled by the pain.